Answer
a). $2$
b). $29$
c). $29$
d). $<0,12,10>$
e). $4$
Work Step by Step
$\mathbf{u}=<2,-3,4>$ and $\mathbf{v}=<0,6,5>$
a). $\mathbf{u}\cdot\mathbf{v}=2\times0+-3\times6+4\times5=0+-18+20=2$
b). $\mathbf{u}\cdot\mathbf{u}=2\times2+-3\times(-3)+4\times4=29$
c). $\|\mathbf{u}\|^2= \mathbf{u}\cdot\mathbf{u}=29$
d). $(\mathbf{u}\cdot\mathbf{v})\mathbf{v}=2\mathbf{v}=<0,12,10>$
e). $\mathbf{u}\cdot(2\mathbf{v})=<2,-3,4>\cdot<0,12,10>=0+-36+40=4$
